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One of our grad students (Dimitria) recently presented findings at the 2024 IEEE International Symposium on Systems Engineering (ISSE) in Perugia, Italy. This new work builds off some of our earlier investigations into emergent leminscate traectories by providing a more general solution, applicable to a wide range of closed-curve trajectories. Abstract This work investigates the self-organization of multi-agent systems into closed trajectories, a common requirement in unmanned aerial vehicle (UAV) surveillance tasks. In such scenarios, smooth, unbiased control signals save energy and mitigate mechanical strain. We propose a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories. Central to our approach is the formulation of an injective virtual embedding induced by rotations from the actual agent positions. This embedding serves as a structure-preserving map around which all agent stabilize their relative positions and permits the use of well-established linear control techniques. We construct the embedding such that it is topologically equivalent to the desired trajectory (i.e., a homeomorphism), thereby preserving the stability characteristics. We demonstrate the versatility of this approach through implementation on a swarm of Quanser QDrone quadcopters. Results demonstrate the quadcopters self-organize into the desired trajectory while maintaining even separation. ...

I have finally checked off the career milestone of publishing in an IEEE Transactions journal. I was inspired to develop this solution after watching a flock of birds attack a squirrel on my neighbour’s roof. I noticed the birds produced a modified figure-eight pattern, which allowed them to dive down and attack the squirrel one-after-the-other in a coordinated manner. Abstract Inspired by the natural mobbing behavior of birds, this work presents a novel, quasi-distributed swarming strategy called the Dynamic Lemniscatic Arch. It resolves the problem of producing globally-stable, evenly-spaced lemniscate (or, figure-eight) trajectories while relying on local interactions only. Such trajectories are advantageous in applications where energy consumption and mechanical strain must be minimized. Previous work in lemniscate curves has typically relied on predetermined trajectories, rather than on the emergent structure of the swarm. Furthermore, we enrich the traditional 2-dimensional lemniscate plane curve structure by forming an arch in the third dimension. This arch provides more consistent coverage in surveillance type tasks and, with minor variations in parameters, can be used to produce mobbing behavior. The technique relies on time-varying quaternion rotations linked to the positions of dynamically induced virtual agents. We provide a mathematical proof of stability, which demonstrates the swarm converges to the desired geometry. Simulations show that the strategy performs well with multiple agents and in numerous different configurations. ...